Kinetics of copolymerization

Typically, the kinetics of ring-opening copolymerization is analyzed in terms of the four equations, set with all reactions being irreversible. The aim of a such an analysis is to determine the reactivity ratios ri = ku/ku and r2 = k22/k2i by means of the approaches elaborated by Mayo and Lewis or Finneman and Ross, or perhaps by Kelen and Tudos. Provided that the homopolymerization rate constants (fen and fe22 are known from the homopolymerization studies, under otherwise identical conditions-and assuming that the same values are valid in copolymerization (this is not necessarily tme for ionic or coordination ROP)-the crosspropagation rate constants (fen and fe2i) can eventually be determined. 

However, with the exception of copolymerization of the three- and/or four-membered comonomers, the copolymerization of higher rings is expected to be reversible, such that four additional homo- or cross-depropagation reactions must be added (kinetic Equation 1.44). In such a situation, the traditional methods of kinetic analysis must be put on hold , as a numerical solving of the corresponding differential equations is necessary. Moreover, depending on the selectivity of the active centers, any reversible transfer reactions can interfere to various degrees with the copolymerization process. Thus, the kinetically controlled microstructure of the copolymer may differ substantially from that at equilibrium (cf Section 1.2.4). 

Instractive example of the copolymerization involving monomer propagating reversibly comes from the L,L-lactide (LA)/e aprolactone (CL) comonomers pair [181, 182). Recent analysis of this copolymerization system, by means of the numerical integration method [183], revealed that the comonomers reactivity ratios can be controlled by the configuration of the active species [184]. Thus, using initiator of various stereochemical compositions a broad spectrum of copolymers 

Random and Alternating Copolymers a) Mechanism and Kinetics of Copolymerization 

Extensive work on radical copolymerization has shown that the composition in a binary copolymer, consisting of monomers Mi and M2, is determined by four rate constants ky for a propagating chain ending with adding to monomer Mj. 

The Mayo-Lewis equation expressing the copolymer composition can be derived from these four elementary reactions. It reads 

However, ionic copolymerizations are much more selective than radical copolymerizations and the number of copolymer pairs which undergo ionic copolymerization is relatively limited. Cross-propagation rarely occurs between monomer pairs 

Thus a log-log plot of the apparent copolymer composition ratio against the monomer feed ratio should yield a straight line with slope two. In fact, a slope near two was observed for several comonomer pairs with different polarities. 

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Any understanding of the kinetics of copolymerization and the structure of copolymers requires a knowledge of the dependence of the initiation, propagation and termination reactions on the chain composition, the nature of the monomers and radicals, and the polymerization medium. This section is principally concerned with propagation and the effects of monomer reactivity on composition and monomer sequence distribution. The influence of solvent and complcxing agents on copolymerization is dealt with in more detail in Section 8.3.1. 

The influence of penultimate units on the kinetics of copolymerization and the composition of copolymers was first considered in a formal way by Merz et al and Ham.8 They consider eight propagation reactions (Scheme 7.2). 

In early work, it was assumed that the rate constant for termination was determined by the monomer unit at the reacting chain ends. The kinetics of copolymerization were then dictated by the rate of initiation, the rates of the four propagation reactions (Scheme 7.1) and rales of three termination reactions... 

In evaluating the kinetics of copolymerization according to the chemical control model, it is assumed that the termination rate constants k,AA and A,Br are known from studies on homopolymerization. The only unknown in the above expression is the rate constant for cross termination (AtAB)- The rate constant for this reaction in relation to klAA and kmB is given by the parameter . 

The ends of polymer chains are often not representative of the overall chain composition. This arises because the initiator and transfer agent-derived radicals can show a high degree of selectivity for reaction with a particular monomer type (Section 3.4). Similarly, there is specificity in chain tennination. Transfer agents show a marked preference for particular propagating species (Section 6.2.2 and 6.2.3). The kinetics of copolymerization are such that the probability for termination of a given chain by radical-radical reaction also has a marked dependence on the nature of the last added units (Section 7.4.3). 

THF copolymerizes readily with other cyclic ethers such as oxides and oxetanes. The comonomers used include ethylene oxide (67), propylene oxide (99,100), epichlorohydrin (ECH) (101,102), phenyl glycidyl ether (102), 3.3-bis(chloromethyl) oxetane (BCMO) (25, 98, 101, 103) and 3-methyl-3-chloromethyl oxetane (103). Just as in THF homo-polymerization, a large variety of catalysts have veen used. In many cases the kinetics of copolymerization have been studied. Table 22 summarizes the monomer reactivity ratios, rx (THF), and r2 (comonomer) which have... 

In studies of the kinetics of copolymerization of cyclic compounds the Mayo—Lewis equations [150] for kinetics of copolymerization have been applied, often with deserved caution. Many monomer reactivity ratios have been derived in this way. A large number of them have been summarized previously [7, 151] and we will not repeat them here nor attempt to update the lists. Instead we shall concentrate on some of the factors that seem to be important in regulating the copolymerizations and on some of the newer approaches that have been suggested for dealing with the complicated kinetics and give only a few examples of individual rate studies. 

NIR spectrophotometry in the region from 8000 to 4000 cm-1 was used to measure the kinetics of copolymerization of an aromatic bismaleimide (72) derived from an aromatic diamine (e.g. 5a), taking place at 160 to 180 °C. The following NIR spectral ranges were useful for this study primary amine first overtones (vn h) at 7000 to 6400 cm-1, double bond first overtone (vc=c-h) at 6100 cm-1, aromatic first overtones (vc-h) at 6000 to 5750 cm-1, aliphatic first overtones (vc-h) at 5750 to 5350 cm-1 and primary aromatic amine combination bands first overtones (vn h + <5nh2) at 5150 to 4800 cm-1. The process consisted mainly of a second-order Michael addition, as depicted in equation 14, and not the plausible imide opening to yield a maleic dianilide (119), as shown in equation 15. A Michael addition between maleimide moieties and secondary amine moieties present in the products (118) also takes place, however at a rate of about one fourth of that of the primary amine moieties. To improve the SNR of the measurements, usually the results of... 

The composition of a copolymer formed in an addition-polymerization reaction will not simply be the composition of the feed M1/M2 since the reactivity of the two monomers to the initiating and propagating species (whether free radical, anion or cation) may differ. The kinetics of copolymerization is a suitable route for the introduction of the concepts since this then allows the composition of the copolymers to be described systematically. Free-radical reactions are those mostly encountered in reactive processing and are considered below. 

Section 3 deals with the procedures used to obtain information on the sequence distribution in C2-C3 copolymers and hence to throw light on the kinetics of copolymerization. From this point of view, the situation of C2-C3 copolymers is quite favourable, since their IR spectrum exhibits bands characteristic of sequences of different lengths of both monomers. Even more care is needed in establishing correlations between band intensities and sequence distribution than in setting up analytical methods. 

All IR investigations of sequence distribution so far published rely on the terminal copolymerization model, which assumes that the kinetics of copolymerization are governed only by the probability that monomer units from the feed will be added to the last unit of the growing chain, and that there is only one active site present in the catalyst system, whether homogeneous or heterogeneous. As will be shown later (Section 3.4), this is only an approximation multiple active species are formed by many soluble Ziegler-Natta catalysts, so that the product of reactivity ratios determined from the normal copolymerization equation does not always exactly predict the actual sequence distribution in the copolymer. 

The kinetics of copolymerization and the microstructure of copolymers can be markedly influenced by the addition of Lewis acids. In particular, Lewis acids are effective in enhancing the tendency towards alternation in copolymerization of donor-acceptor monomer pairs and can give dramatic enhancements in the rate of copolymerization and much higher molecular weights than are observed for similar conditions without the Lewis acid. Copolymerizations where the electron deficient monomer is an acrylic monomer e.g. AN, MA, MMA) and the electron rich monomer is S or a diene have been the most widely studied." Strictly alternating copolymers of MMA and S can be prepared in the presence of, for example, dictliylaluminum scsquichloridc. In the absence of Lewis acids, there is only a small tendency for alternation in MAA-S copolymerization terminal model reactivity ratios are ca 0.51 and 0.49 - Section 7.3.1.2.3. Lewis acids used include EtAlCT, Et.AlCL ElALCL, ZnCT, TiCU, BCl- LiC104 and SnCL. 

The kinetics of copolymerization or curing of epoxy resins with cyclic anhydrides initiated by tertiary amines was investigated by chemical analysis 52,65,73,74,90) differential scanning calorimetry isothermal methods electric methods , dynamic differential thermal analysis , IR spectroscopy dilatometry or viscometry Results of kinetic measurements and their interpretation differ most authors agree, however, that the copolymerization is of first order with respect to the tertiary amine. 

The kinetics of copolymerization provides a partial explanation for the copolymerization behavior of styrenes with dienes. One useful aspect of living anionic copolymerizations is that stable carbanionic chain ends can be generated and the rates of their crossover reactions with other monomers measured independently of the copolymerization reaction. Two of the four rate constants involved in copolymerization correspond at least superficially to the two homopolymerization reactions of butadiene and styrene, for example, and k, respectively. The other... 

P. Wittmer, Kinetics of copolymerization, Makromol. Chem., Suppl. 3, 129 (1979). 

The copolymerization equation (22-14) was originally derived with the equations in (22-1) on considering that Vi = —d[Mi ]/dt together with the condition i i2 = 1 21- This assumption certainly seems to be fulfilled satisfactorily for free radical polymerizations, but it is doubtful in the case of ionic copolymerizations. The preceding statistical derivation holds good without assuming that V12 = 21 thus shows at the same time that the copolymerization equation must also apply to ionic copolymerizations when conditions 1-5 are fulfilled. The copolymerization equation also provides no information about the kinetics of copolymerization. 

Ttldds and Vertes extend their smes of publications on the kinetics of copolymerization with an examination of the dependence of the initiation rate constant on the monomer feed ratio in the copolymerization of acrylonitrile and methyl methacrylate at various temperatures. In measuring the overall rate of polymerization of styrene with ethylacrylate in benzene, Fehervari et al ... 

It was shown that penultimate effect modify the kinetics of copolymerization and given a method which allows to express the copolymerization equation, in the general case. 

Ureta et al. [128] reported that the kinetics of copolymerization of styrene and DPE with sodium as counterion in THF were complicated by the reversibility of the addition of styrene to the polymeric 1,1-diphenylmethyl carba-nion as shown in Eq. (28) ... 

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